1. The simulation of news and insiders'
influence on stock-market prices
dynamics in non-linear model
Victor Romanov, Oksana Naletova, Eugenia Pantileeva, Alexander Federyakov
Plekhanov Russian Academy of Economics
Computational Finance 2006
27 – 29 June 2006
London, UK
2. There exist two kinds of traders’ strategies
F- trader strategy: N-trader strategy:
ef t cF (vt xt )3 (vt xt )3 ent cN ( xt yt ) xt yt
vt vt 1 h t yt xt 1 (1 ) yt 1
The aggregate excess demand:
et wt ef t (1 wt )ent
Dynamic prices’ adjustment:
xt 1 xt bet bwt ef t b(1 wt )ent
wt
Share of the two types of investors : wt 1
wt (1 wt )e gRt
t 1 t 1 t 1 t 1
R - the past relative return Rt [ xt ef
j t k
j x ef
j t k
j j ] / k [ xt en
j t k
j x en ] / k
j t k
j j
3. Common view of program interface with graphic representation of
artificial time series generated by the program and simulating
dollar/ruble exchange
The interface permits to make the substitution parameter values into the model:
alfa, Cf, Cn, w1, g, b, k, Insiders share, q, S, Noise, Strength, u, h, v1, Count, bad/good
slide and to overview the variables values.
4. Non-linear oscillation The strange attractor
The real
head
and
shoulder
pattern
This output looks like head and shoulder pattern
6. vj+1 := vj +( h * (Exp Qj - 1) / (Exp Qj + 1)) + εj
The price fundamental value is rising up The price fundamental value is falling down
with “good” news with “bad” news
7. eins t q * ( xt xt 1 ) 2 The insiders’ return
The total return including
R Rins t , if _ R 0 insiders
Rt 1 { t
Rt Rins t , if _ Rt 0
The insiders’ past relative
t 1 t 1 return
Rins t ( x j eins
j t k
j x eins
j t k
j j )/k
et wt ef t (1 w l ) * ent l * eins t Excess demand now
The combined news and insiders’ influence on the price fundamental value
vt (h * Exp ( s ( Rins t /( Rt Rins t )))) * ( Exp (Qt ) 1) /( Exp (Qt ) 1), if ( Rt Rins t ) 0
vinst 1 {
vt (h * ( ExpQt 1) /( ExpQt 1)) t , if ( Rt Rins t ) 0
8. Insiders impact on the assets market price Insiders’ super profit implying
market collapse
Insiders past relative return Market prices behavior in proximity of
crash point
9. 26.5
26
25.5
25
24.5 Ряд1
24
23.5
23
22.5
0 20 40 60 80 100 120 140 160 180 200
Prices’ behavior with insiders
Real data USD/ruble change rate
data during Russian default for
period 05.03.1999 – 01.11.1999
Insiders’ return
10. 18
16
14
12
10
Ряд1
8
6
4
2
0
0 100 200 300 400 500 600
Insiders impact on the assets market
price For comparison Yukos
actions open prices for
period from 13.10.2003
to 26.11.2004
Insiders past relative return
11. I Input neurons
N
Output neurons
P
U
T
D
A
T
A
12. x(1)+1) x(2)+ x(3)+ x(4)+ x(5)+ x(6)+ x(N)+
x(1) x(2) x(3) x(4)
x(2) x(3) x(4) x(5)
x(3) x(4) x(5) x(6)
x(4) x(5) x(6) x(7) Kohonen Net input data window sliding along time series
………………………………
x(N-1) x(N-2) x(N-1) x(N)
The time series is cut into pieces to
arrange sliding data window
13.
14. 0,4
0,3
0,2
0,1
0
0 5 10 15 20 25 30 35
-0,1
-0,2
-0,3
Chart pattern class A Chart pattern class B
31 38.5
38
30.5
37.5
30
37
29.5
36.5
29 36
35.5
28.5
35
28
34.5
27.5
34
27 33.5
0 100 200 300 400 500 600 0 100 200 300 400 500 600
The arrows indicate places where Kohonen Net recognize patterns of classes A and B
![There exist two kinds of traders’ strategies
F- trader strategy: N-trader strategy:
ef t cF (vt xt )3 (vt xt )3 ent cN ( xt yt ) xt yt
vt vt 1 h t yt xt 1 (1 ) yt 1
The aggregate excess demand:
et wt ef t (1 wt )ent
Dynamic prices’ adjustment:
xt 1 xt bet bwt ef t b(1 wt )ent
wt
Share of the two types of investors : wt 1
wt (1 wt )e gRt
t 1 t 1 t 1 t 1
R - the past relative return Rt [ xt ef
j t k
j x ef
j t k
j j ] / k [ xt en
j t k
j x en ] / k
j t k
j j](data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7)